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# 3 digit numbers

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Senior Manager
Joined: 22 Jun 2004
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3 digit numbers [#permalink]  13 Sep 2004, 20:49
How many 3 digit numbers are divisible by 6?

_________________

Awaiting response,

Thnx & Rgds,
Chandra

Senior Manager
Joined: 22 Feb 2004
Posts: 350
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150.
I did it with a combination of some unconventional logic and brute force..but did it in less than 2 min..wud like to know any other sophisticated method
Director
Joined: 20 Jul 2004
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We can use simple arithmetic progression formula.

n = (l-a)/d + 1

l = 996
a = 102
d = 6
n = (996-102)/6 + 1 = 150
Senior Manager
Joined: 22 Feb 2004
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Oh god..
Actually, AP, GP are not in the syllabus of GMAT..so i forget about them and tend not to use them.
But yes, if one can apply them..one shud do that.At the end of the day, nobody is going to know how u arrived at right answer.
Senior Manager
Joined: 22 Jun 2004
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Location: Bangalore, India
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hardworker_indian,

It is a good method.

The following method is intuitive, I believe.

999 is the highest in value for 3 digit numbers. Divide it with 6 and take the integer part ONLY to get the total number of numbers divisible by 6.
=> 999/6 = 166
However, it does include numbers up to 100 which we donot need.
=> 100/6 = 16

So, the required number of 3 digit numbers = 166-16 = 150.

hardworker_indian wrote:
We can use simple arithmetic progression formula.

n = (l-a)/d + 1

l = 996
a = 102
d = 6
n = (996-102)/6 + 1 = 150

_________________

Awaiting response,

Thnx & Rgds,
Chandra

Manager
Joined: 07 Sep 2004
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150 is not accurate.

The 3 digit number includes also 006,012,..... . No mention in the text that the hundreth digit is not a 0 digit.

[/quote]
Senior Manager
Joined: 22 Jun 2004
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Location: Bangalore, India
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As per my understanding 3 digit numbers are from 100 to 999.

If I were to take your suggestion, I can never define the number of digits at all. Say,
1 - one digit
01 - two digits
001 - three digits
0001 - four digits
.
.
.
.
.

This can go on and on and on. In essense, all the above numbers represent the single digit 1, though.

Any other opinions on the query raised by 'amernassar'.

amernassar wrote:
150 is not accurate.

The 3 digit number includes also 006,012,..... . No mention in the text that the hundreth digit is not a 0 digit.

[/quote]
_________________

Awaiting response,

Thnx & Rgds,
Chandra

GMAT Club Legend
Joined: 07 Jul 2004
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A number is divisible by 6 if it is divisble by both 2 and 3

Numbers divisible by 2 = multiple of 2, 2,4,6...
Numbers divisible by 3 = multiple of 3, 3,6,9,...

So the number number be a multiple of 6 (LCM)

From 100-999, there are 900 numbrs. Numbers divisible by 6 = 900/6 = 150
(Because for every group of 6 numbers starting from 100, only 1 is divisible by 6)
CEO
Joined: 15 Aug 2003
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amernassar wrote:
150 is not accurate.

The 3 digit number includes also 006,012,..... . No mention in the text that the hundreth digit is not a 0 digit.

[/quote]

you may be the first member from Lebanon. welcome !
Manager
Joined: 07 Sep 2004
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let me elaborate on this matter

we are dealing with a 3 digit number. 012 is a 3 digit number because it has the digits 0,1,2 . on the other hand 0024 is a 4 digit number.

imagine it as a digital locker of a suitcase with 3 numbers comprised as digits

for that we also have including the 3 digit numbers from 100 to 999 the following numbers

000,006,012,024,030,036,042,048,054,060,066,072,078,084,090,096 (these are in fact the 16 that was subtracted from 166 to get 150)

the 0 in the hundreth place need to be considered

In order for the question to be 150 , it should be mentioned thet the hundredth number is not zero

I may have seen some problems where they say that the hundredth digit is non-zero to clarify matters more.

Best regards
Amer
Director
Joined: 20 Jul 2004
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I understand your point. Good example on locker code.

But, in general, when thay say a "two digit number", that means 10x+y where x <> 0. Example: 11, 23, 99. Not 09 or 01.

You can think of zero as a valid digit in the front of the number (say, 09) only when you consider that as a text. When you consider that as a number, it is a single digit (9). (My sybase knowledge comes handy atlast )

You may corelate this with typing a number in MS excel with property defined as text and number.
SVP
Joined: 16 Oct 2003
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150 and we are talking about pure maths and not applied maths.
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